The long-running patent battles between Minnesota’s two leading recreational vehicle manufacturers has some new chapters.

Polaris filed a lawsuit in late December, accusing Plymouth-based Arctic Cat of illegally using Polaris’ 501 Patent to make side-by-side recreational vehicles. Arctic Cat filed a response this week, insisting it infringed upon no patents held by Medina-based Polaris Industries.

Earlier this month, Arctic Cat filed three lawsuits of its own, accusing Polaris of infringing on three of its patents relating to a power distribution module, its 2010 tandem four-wheel vehicle and textured fenders.

Polaris declined Friday to comment on pending litigation.

Arctic Cat officials issued a statement Friday saying Arctic Cat doesn’t infringe any valid or enforceable claim of Polaris’ 501 Patent.

Polaris’ December lawsuit and accompanying documents said Polaris submitted its 501 Patent application in 2010 and that the U.S. Patent Office formally issued it to Polaris last month. Polaris claims its design for a side-by-side off-road four-wheel vehicle was copied and sold as Arctic Cat’s Wildcat Sport and Wildcat Trail off-road vehicles. Polaris is asking for royalties, attorney fees and an injunction against Arctic Cat from using the design again.

In its response to the lawsuit, Arctic Cat has demanded a jury trial.

“Arctic Cat denies that Polaris is entitled to any of the relief sought by its complaint,” the court filing said. “Arctic Cat has not infringed, directly or indirectly, any valid and enforceable claim of the ‘501 Patent.’ ”

Furthermore, the company’s most recent filing said the 501 Patent is invalid.

Both companies have sued each other before.

Polaris sued Arctic Cat in 2013 for patent infringement. Arctic Cat counter sued, and the court dismissed that counter lawsuit in August 2015.

Polaris sued Arctic Cat in 1999 for allegedly infringing on a patent for an adjustable snowmobile suspension.

In 2003, Arctic Cat used Polaris for allegedly infringing on Arctic Cat’s exhaust temperature ignition timing patent, which was used to make the high-performance engines of racing snowmobiles.

Arctic Cat and Polaris are operating in an increasingly difficult market for off-road vehicles and each warned the climate would continue at least through the end of March.

Despite that, Arctic Cat is continuing a turnaround plan that includes plant expansions and more aggressive new product offerings. Arctic Cat’s stock rose $1.30 a share Friday to close at $12.31, a level far below its 52-week high of 39.72 per share.

Polaris’s stock rose $4.23 Friday to close at $73.84, which is far off its 52-week high of $158 per share.